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<div class="title">XprHelper.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2006-2008 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#ifndef EIGEN_XPRHELPER_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="preprocessor">#define EIGEN_XPRHELPER_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#include &quot;../InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> IndexDest, <span class="keyword">typename</span> IndexSrc&gt;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="keyword">inline</span> IndexDest convert_index(<span class="keyword">const</span> IndexSrc&amp; idx) {</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="comment">// for sizeof(IndexDest)&gt;=sizeof(IndexSrc) compilers should be able to optimize this away:</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  eigen_internal_assert(idx &lt;= NumTraits&lt;IndexDest&gt;::highest() &amp;&amp; <span class="stringliteral">&quot;Index value to big for target type&quot;</span>);</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;  <span class="keywordflow">return</span> IndexDest(idx);</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;}</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment">// true if T can be considered as an integral index (i.e., and integral type or enum)</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>is_valid_index_type</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;{</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <span class="keyword">enum</span> { value = internal::is_integral&lt;T&gt;::value || std::is_enum&lt;T&gt;::value</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  };</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;};</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160; </div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment">// true if both types are not valid index types</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> RowIndices, <span class="keyword">typename</span> ColIndices&gt;</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="keyword">struct </span>valid_indexed_view_overload {</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  <span class="keyword">enum</span> { value = !(internal::is_valid_index_type&lt;RowIndices&gt;::value &amp;&amp; internal::is_valid_index_type&lt;ColIndices&gt;::value) };</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;};</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="comment">// promote_scalar_arg is an helper used in operation between an expression and a scalar, like:</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="comment">//    expression * scalar</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="comment">// Its role is to determine how the type T of the scalar operand should be promoted given the scalar type ExprScalar of the given expression.</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="comment">// The IsSupported template parameter must be provided by the caller as: internal::has_ReturnType&lt;ScalarBinaryOpTraits&lt;ExprScalar,T,op&gt; &gt;::value using the proper order for ExprScalar and T.</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="comment">// Then the logic is as follows:</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="comment">//  - if the operation is natively supported as defined by IsSupported, then the scalar type is not promoted, and T is returned.</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="comment">//  - otherwise, NumTraits&lt;ExprScalar&gt;::Literal is returned if T is implicitly convertible to NumTraits&lt;ExprScalar&gt;::Literal AND that this does not imply a float to integer conversion.</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="comment">//  - otherwise, ExprScalar is returned if T is implicitly convertible to ExprScalar AND that this does not imply a float to integer conversion.</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="comment">//  - In all other cases, the promoted type is not defined, and the respective operation is thus invalid and not available (SFINAE).</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExprScalar,<span class="keyword">typename</span> T, <span class="keywordtype">bool</span> IsSupported&gt;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="keyword">struct </span>promote_scalar_arg;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> S,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;<span class="keyword">struct </span>promote_scalar_arg&lt;S,T,true&gt;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;{</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  <span class="keyword">typedef</span> T type;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;};</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;<span class="comment">// Recursively check safe conversion to PromotedType, and then ExprScalar if they are different.</span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExprScalar,<span class="keyword">typename</span> T,<span class="keyword">typename</span> PromotedType,</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <span class="keywordtype">bool</span> ConvertibleToLiteral = internal::is_convertible&lt;T,PromotedType&gt;::value,</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  <span class="keywordtype">bool</span> IsSafe = NumTraits&lt;T&gt;::IsInteger || !NumTraits&lt;PromotedType&gt;::IsInteger&gt;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;<span class="keyword">struct </span>promote_scalar_arg_unsupported;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160; </div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="comment">// Start recursion with NumTraits&lt;ExprScalar&gt;::Literal</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> S,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;<span class="keyword">struct </span>promote_scalar_arg&lt;S,T,false&gt; : promote_scalar_arg_unsupported&lt;S,T,typename NumTraits&lt;S&gt;::Literal&gt; {};</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;<span class="comment">// We found a match!</span></div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> S,<span class="keyword">typename</span> T, <span class="keyword">typename</span> PromotedType&gt;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;<span class="keyword">struct </span>promote_scalar_arg_unsupported&lt;S,T,PromotedType,true,true&gt;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;{</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  <span class="keyword">typedef</span> PromotedType type;</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;};</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160; </div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;<span class="comment">// No match, but no real-to-integer issues, and ExprScalar and current PromotedType are different,</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;<span class="comment">// so let&#39;s try to promote to ExprScalar</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExprScalar,<span class="keyword">typename</span> T, <span class="keyword">typename</span> PromotedType&gt;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;<span class="keyword">struct </span>promote_scalar_arg_unsupported&lt;ExprScalar,T,PromotedType,false,true&gt;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;   : promote_scalar_arg_unsupported&lt;ExprScalar,T,ExprScalar&gt;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;{};</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160; </div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;<span class="comment">// Unsafe real-to-integer, let&#39;s stop.</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> S,<span class="keyword">typename</span> T, <span class="keyword">typename</span> PromotedType, <span class="keywordtype">bool</span> ConvertibleToLiteral&gt;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="keyword">struct </span>promote_scalar_arg_unsupported&lt;S,T,PromotedType,ConvertibleToLiteral,false&gt; {};</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">// T is not even convertible to ExprScalar, let&#39;s stop.</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> S,<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="keyword">struct </span>promote_scalar_arg_unsupported&lt;S,T,S,false,true&gt; {};</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">//classes inheriting no_assignment_operator don&#39;t generate a default operator=.</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="keyword">class </span>no_assignment_operator</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;{</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;    no_assignment_operator&amp; operator=(<span class="keyword">const</span> no_assignment_operator&amp;);</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    EIGEN_DEFAULT_COPY_CONSTRUCTOR(no_assignment_operator)</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;    EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(no_assignment_operator)</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;};</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> I1, <span class="keyword">typename</span> I2&gt;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;<span class="keyword">struct </span>promote_index_type</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;{</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;(<span class="keyword">sizeof</span>(I1)&lt;<span class="keyword">sizeof</span>(I2)), I2, I1&gt; type;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;};</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> Value&gt; <span class="keyword">class </span>variable_if_dynamic</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;{</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;    EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(variable_if_dynamic)</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">explicit</span> variable_if_dynamic(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;    T value() { <span class="keywordflow">return</span> T(Value); }</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;    <span class="keyword">operator</span> T()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> T(Value); }</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;    <span class="keywordtype">void</span> setValue(T v)<span class="keyword"> const </span>{ EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;};</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">class </span>variable_if_dynamic&lt;T, <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>&gt;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;{</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;    T m_value;</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">explicit</span> variable_if_dynamic(T value = 0) EIGEN_NO_THROW : m_value(value) {}</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T value()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_value; }</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">operator</span> T()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_value; }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> setValue(T value) { m_value = value; }</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;};</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160; </div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> Value&gt; <span class="keyword">class </span>variable_if_dynamicindex</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;{</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">explicit</span> variable_if_dynamicindex(T v) { EIGEN_ONLY_USED_FOR_DEBUG(v); eigen_assert(v == T(Value)); }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    EIGEN_DEVICE_FUNC <span class="keyword">static</span> EIGEN_STRONG_INLINE EIGEN_CONSTEXPR</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    T value() { <span class="keywordflow">return</span> T(Value); }</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    <span class="keywordtype">void</span> setValue(T) {}</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;};</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">class </span>variable_if_dynamicindex&lt;T, <a class="code" href="namespaceEigen.html#a73c597189a4a99127175e8167c456fff">DynamicIndex</a>&gt;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;{</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    T m_value;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    EIGEN_DEVICE_FUNC variable_if_dynamicindex() { eigen_assert(<span class="keyword">false</span>); }</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keyword">explicit</span> variable_if_dynamicindex(T value) : m_value(value) {}</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    EIGEN_DEVICE_FUNC T EIGEN_STRONG_INLINE value()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_value; }</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE <span class="keywordtype">void</span> setValue(T value) { m_value = value; }</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;};</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>functor_traits</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;{</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  <span class="keyword">enum</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  {</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    Cost = 10,</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    PacketAccess = <span class="keyword">false</span>,</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    IsRepeatable = <span class="keyword">false</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;  };</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;};</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160; </div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>packet_traits;</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160; </div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>unpacket_traits;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> Size, <span class="keyword">typename</span> PacketType,</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;         <span class="keywordtype">bool</span> Stop = Size==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> || (Size%unpacket_traits&lt;PacketType&gt;::size)==0 || is_same&lt;PacketType,<span class="keyword">typename</span> unpacket_traits&lt;PacketType&gt;::half&gt;::value&gt;</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="keyword">struct</span> find_best_packet_helper;</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="keyword">template</span>&lt; <span class="keywordtype">int</span> Size, <span class="keyword">typename</span> PacketType&gt;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="keyword">struct </span>find_best_packet_helper&lt;Size,PacketType,true&gt;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;{</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;  <span class="keyword">typedef</span> PacketType type;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;};</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160; </div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> Size, <span class="keyword">typename</span> PacketType&gt;</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="keyword">struct </span>find_best_packet_helper&lt;Size,PacketType,false&gt;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;{</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> find_best_packet_helper&lt;Size,typename unpacket_traits&lt;PacketType&gt;::half&gt;::type type;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;};</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160; </div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> Size&gt;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="keyword">struct </span>find_best_packet</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;{</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> find_best_packet_helper&lt;Size,typename packet_traits&lt;T&gt;::type&gt;::type type;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;};</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160; </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="preprocessor">#if EIGEN_MAX_STATIC_ALIGN_BYTES&gt;0</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;constexpr <span class="keyword">inline</span> <span class="keywordtype">int</span> compute_default_alignment_helper(<span class="keywordtype">int</span> ArrayBytes, <span class="keywordtype">int</span> AlignmentBytes) {</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;  <span class="keywordflow">if</span>((ArrayBytes % AlignmentBytes) == 0) {</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="keywordflow">return</span> AlignmentBytes;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (EIGEN_MIN_ALIGN_BYTES&lt;AlignmentBytes) {</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    <span class="keywordflow">return</span> compute_default_alignment_helper(ArrayBytes, AlignmentBytes/2);</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;    <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;  }</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;}</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;<span class="comment">// If static alignment is disabled, no need to bother.</span></div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;<span class="comment">// This also avoids a division by zero</span></div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;constexpr <span class="keyword">inline</span> <span class="keywordtype">int</span> compute_default_alignment_helper(<span class="keywordtype">int</span> ArrayBytes, <span class="keywordtype">int</span> AlignmentBytes) {</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  EIGEN_UNUSED_VARIABLE(ArrayBytes);</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  EIGEN_UNUSED_VARIABLE(AlignmentBytes);</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;}</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160; </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> Size&gt; <span class="keyword">struct </span>compute_default_alignment {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  <span class="keyword">enum</span> { value = compute_default_alignment_helper(Size*<span class="keyword">sizeof</span>(T), EIGEN_MAX_STATIC_ALIGN_BYTES) };</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;};</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>compute_default_alignment&lt;T,<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>&gt; {</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;  <span class="keyword">enum</span> { value = EIGEN_MAX_ALIGN_BYTES };</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;};</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160; </div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar_, <span class="keywordtype">int</span> Rows_, <span class="keywordtype">int</span> Cols_,</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;         <span class="keywordtype">int</span> Options_ = <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea">AutoAlign</a> |</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;                          ( (Rows_==1 &amp;&amp; Cols_!=1) ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;                          : (Cols_==1 &amp;&amp; Rows_!=1) ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a></div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;                          : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION ),</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;         <span class="keywordtype">int</span> MaxRows_ = Rows_,</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;         <span class="keywordtype">int</span> MaxCols_ = Cols_</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;&gt; <span class="keyword">class</span> make_proper_matrix_type</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;{</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;      IsColVector = Cols_==1 &amp;&amp; Rows_!=1,</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;      IsRowVector = Rows_==1 &amp;&amp; Cols_!=1,</div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;      Options = IsColVector ? (Options_ | <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>) &amp; ~<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a></div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;              : IsRowVector ? (Options_ | <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>) &amp; ~<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a></div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;              : Options_</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    };</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    <span class="keyword">typedef</span> Matrix&lt;Scalar_, Rows_, Cols_, Options, MaxRows_, MaxCols_&gt; type;</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;};</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;constexpr <span class="keyword">inline</span> <span class="keywordtype">unsigned</span> compute_matrix_flags(<span class="keywordtype">int</span> Options) {</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="keywordtype">unsigned</span> row_major_bit = Options&amp;<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a> ? <a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a> : 0;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="comment">// FIXME currently we still have to handle DirectAccessBit at the expression level to handle DenseCoeffsBase&lt;&gt;</span></div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="comment">// and then propagate this information to the evaluator&#39;s flags.</span></div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="comment">// However, I (Gael) think that DirectAccessBit should only matter at the evaluation stage.</span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="group__flags.html#gabf1e9d0516a933445a4c307ad8f14915">DirectAccessBit</a> | <a class="code" href="group__flags.html#gae2c323957f20dfdc6cb8f44428eaec1a">LvalueBit</a> | NestByRefBit | row_major_bit;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;}</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160; </div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;constexpr <span class="keyword">inline</span> <span class="keywordtype">int</span> size_at_compile_time(<span class="keywordtype">int</span> rows, <span class="keywordtype">int</span> cols) {</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;  <span class="keywordflow">return</span> (rows==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> || cols==<a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a>) ? <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> : rows * cols;</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;}</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160; </div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> XprType&gt; <span class="keyword">struct </span>size_of_xpr_at_compile_time</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;{</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="keyword">enum</span> { ret = size_at_compile_time(traits&lt;XprType&gt;::RowsAtCompileTime, traits&lt;XprType&gt;::ColsAtCompileTime) };</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;};</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160; </div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;<span class="comment">/* plain_matrix_type : the difference from eval is that plain_matrix_type is always a plain matrix type,</span></div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;<span class="comment"> * whereas eval is a const reference in the case of a matrix</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160; </div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;template&lt;typename T, typename StorageKind = typename traits&lt;T&gt;::StorageKind&gt; <span class="keyword">struct </span>plain_matrix_type;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> BaseClassType, <span class="keywordtype">int</span> Flags&gt; <span class="keyword">struct </span>plain_matrix_type_dense;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>plain_matrix_type&lt;T,Dense&gt;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;{</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> plain_matrix_type_dense&lt;T,typename traits&lt;T&gt;::XprKind, traits&lt;T&gt;::Flags&gt;::type type;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;};</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>plain_matrix_type&lt;T,DiagonalShape&gt;</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;{</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> T::PlainObject type;</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;};</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> Flags&gt; <span class="keyword">struct </span>plain_matrix_type_dense&lt;T,MatrixXpr,Flags&gt;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;{</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;typename traits&lt;T&gt;::Scalar,</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;                traits&lt;T&gt;::RowsAtCompileTime,</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;                traits&lt;T&gt;::ColsAtCompileTime,</div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;                <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea">AutoAlign</a> | (Flags&amp;<a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a> ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a> : <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>),</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;                traits&lt;T&gt;::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;                traits&lt;T&gt;::MaxColsAtCompileTime</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;          &gt; type;</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;};</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160; </div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> Flags&gt; <span class="keyword">struct </span>plain_matrix_type_dense&lt;T,ArrayXpr,Flags&gt;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;{</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;  <span class="keyword">typedef</span> Array&lt;typename traits&lt;T&gt;::Scalar,</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;                traits&lt;T&gt;::RowsAtCompileTime,</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;                traits&lt;T&gt;::ColsAtCompileTime,</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;                <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea">AutoAlign</a> | (Flags&amp;<a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a> ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a> : <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>),</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;                traits&lt;T&gt;::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;                traits&lt;T&gt;::MaxColsAtCompileTime</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;          &gt; type;</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;};</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;<span class="comment">/* eval : the return type of eval(). For matrices, this is just a const reference</span></div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="comment"> * in order to avoid a useless copy</span></div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160; </div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;template&lt;typename T, typename StorageKind = typename traits&lt;T&gt;::StorageKind&gt; <span class="keyword">struct </span>eval;</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160; </div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>eval&lt;T,Dense&gt;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;{</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> plain_matrix_type&lt;T&gt;::type type;</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;<span class="comment">//   typedef typename T::PlainObject type;</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;<span class="comment">//   typedef T::Matrix&lt;typename traits&lt;T&gt;::Scalar,</span></div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="comment">//                 traits&lt;T&gt;::RowsAtCompileTime,</span></div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;<span class="comment">//                 traits&lt;T&gt;::ColsAtCompileTime,</span></div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;<span class="comment">//                 AutoAlign | (traits&lt;T&gt;::Flags&amp;RowMajorBit ? RowMajor : ColMajor),</span></div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;<span class="comment">//                 traits&lt;T&gt;::MaxRowsAtCompileTime,</span></div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;<span class="comment">//                 traits&lt;T&gt;::MaxColsAtCompileTime</span></div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;<span class="comment">//           &gt; type;</span></div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;};</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>eval&lt;T,DiagonalShape&gt;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;{</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> plain_matrix_type&lt;T&gt;::type type;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;};</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160; </div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;<span class="comment">// for matrices, no need to evaluate, just use a const reference to avoid a useless copy</span></div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar_, <span class="keywordtype">int</span> Rows_, <span class="keywordtype">int</span> Cols_, <span class="keywordtype">int</span> Options_, <span class="keywordtype">int</span> MaxRows_, <span class="keywordtype">int</span> MaxCols_&gt;</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;<span class="keyword">struct </span>eval&lt;Matrix&lt;Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_&gt;, Dense&gt;</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;{</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> Matrix&lt;Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_&gt;&amp; type;</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;};</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160; </div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Scalar_, <span class="keywordtype">int</span> Rows_, <span class="keywordtype">int</span> Cols_, <span class="keywordtype">int</span> Options_, <span class="keywordtype">int</span> MaxRows_, <span class="keywordtype">int</span> MaxCols_&gt;</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;<span class="keyword">struct </span>eval&lt;Array&lt;Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_&gt;, Dense&gt;</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;{</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> Array&lt;Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_&gt;&amp; type;</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;};</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160; </div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160; </div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;<span class="comment">/* similar to plain_matrix_type, but using the evaluator&#39;s Flags */</span></div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;template&lt;typename T, typename StorageKind = typename traits&lt;T&gt;::StorageKind&gt; <span class="keyword">struct </span>plain_object_eval;</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160; </div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;<span class="keyword">struct </span>plain_object_eval&lt;T,Dense&gt;</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;{</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> plain_matrix_type_dense&lt;T,typename traits&lt;T&gt;::XprKind, evaluator&lt;T&gt;::Flags&gt;::type type;</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;};</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160; </div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160; </div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;<span class="comment">/* plain_matrix_type_column_major : same as plain_matrix_type but guaranteed to be column-major</span></div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>plain_matrix_type_column_major</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;{</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  <span class="keyword">enum</span> { Rows = traits&lt;T&gt;::RowsAtCompileTime,</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;         Cols = traits&lt;T&gt;::ColsAtCompileTime,</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;         MaxRows = traits&lt;T&gt;::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;         MaxCols = traits&lt;T&gt;::MaxColsAtCompileTime</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;  };</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;typename traits&lt;T&gt;::Scalar,</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;                Rows,</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;                Cols,</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;                (MaxRows==1&amp;&amp;MaxCols!=1) ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a> : <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>,</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;                MaxRows,</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;                MaxCols</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;          &gt; type;</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;};</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160; </div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;<span class="comment">/* plain_matrix_type_row_major : same as plain_matrix_type but guaranteed to be row-major</span></div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>plain_matrix_type_row_major</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;{</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;  <span class="keyword">enum</span> { Rows = traits&lt;T&gt;::RowsAtCompileTime,</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;         Cols = traits&lt;T&gt;::ColsAtCompileTime,</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;         MaxRows = traits&lt;T&gt;::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;         MaxCols = traits&lt;T&gt;::MaxColsAtCompileTime</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;  };</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;typename traits&lt;T&gt;::Scalar,</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;                Rows,</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;                Cols,</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;                (MaxCols==1&amp;&amp;MaxRows!=1) ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a> : <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>,</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;                MaxRows,</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;                MaxCols</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;          &gt; type;</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;};</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160; </div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;<span class="keyword">struct </span>ref_selector</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;{</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    bool(traits&lt;T&gt;::Flags &amp; NestByRefBit),</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;    T <span class="keyword">const</span>&amp;,</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    <span class="keyword">const</span> T</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;  &gt; type;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160; </div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    bool(traits&lt;T&gt;::Flags &amp; NestByRefBit),</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    T &amp;,</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;    T</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;  &gt; non_const_type;</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;};</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160; </div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T1, <span class="keyword">typename</span> T2&gt;</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;<span class="keyword">struct </span>transfer_constness</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;{</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    bool(internal::is_const&lt;T1&gt;::value),</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;    add_const_on_value_type_t&lt;T2&gt;,</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;    T2</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  &gt; type;</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;};</div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160; </div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160; </div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;<span class="comment">// However, we still need a mechanism to detect whether an expression which is evaluated multiple time</span></div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;<span class="comment">// has to be evaluated into a temporary.</span></div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;<span class="comment">// That&#39;s the purpose of this new nested_eval helper:</span></div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;<span class="comment"></span>template&lt;typename T, int n, typename PlainObject = typename plain_object_eval&lt;T&gt;::type&gt; <span class="keyword">struct </span>nested_eval</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;{</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;    ScalarReadCost = NumTraits&lt;typename traits&lt;T&gt;::Scalar&gt;::ReadCost,</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;    CoeffReadCost = evaluator&lt;T&gt;::CoeffReadCost,  <span class="comment">// NOTE What if an evaluator evaluate itself into a temporary?</span></div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;                                                  <span class="comment">//      Then CoeffReadCost will be small (e.g., 1) but we still have to evaluate, especially if n&gt;1.</span></div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;                                                  <span class="comment">//      This situation is already taken care by the EvalBeforeNestingBit flag, which is turned ON</span></div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;                                                  <span class="comment">//      for all evaluator creating a temporary. This flag is then propagated by the parent evaluators.</span></div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;                                                  <span class="comment">//      Another solution could be to count the number of temps?</span></div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    NAsInteger = n == <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#a3163430a1c13173faffde69016b48aaf">HugeCost</a> : n,</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;    CostEval   = (NAsInteger+1) * ScalarReadCost + CoeffReadCost,</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;    CostNoEval = NAsInteger * CoeffReadCost,</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;    Evaluate = (<span class="keywordtype">int</span>(evaluator&lt;T&gt;::Flags) &amp; <a class="code" href="group__flags.html#gaa34e83bae46a8eeae4e69ebe3aaecbed">EvalBeforeNestingBit</a>) || (<span class="keywordtype">int</span>(CostEval) &lt; int(CostNoEval))</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;  };</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160; </div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;Evaluate, PlainObject, typename ref_selector&lt;T&gt;::type&gt; type;</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;};</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160; </div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt;</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;<span class="keyword">inline</span> T* const_cast_ptr(<span class="keyword">const</span> T* ptr)</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;{</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">const_cast&lt;</span>T*<span class="keyword">&gt;</span>(ptr);</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;}</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160; </div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;template&lt;typename Derived, typename XprKind = typename traits&lt;Derived&gt;::XprKind&gt;</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;<span class="keyword">struct </span>dense_xpr_base</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;{</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;  <span class="comment">/* dense_xpr_base should only ever be used on dense expressions, thus falling either into the MatrixXpr or into the ArrayXpr cases */</span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;};</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160; </div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;<span class="keyword">struct </span>dense_xpr_base&lt;Derived, MatrixXpr&gt;</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;{</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;  <span class="keyword">typedef</span> MatrixBase&lt;Derived&gt; type;</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;};</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160; </div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;<span class="keyword">struct </span>dense_xpr_base&lt;Derived, ArrayXpr&gt;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;{</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;  <span class="keyword">typedef</span> ArrayBase&lt;Derived&gt; type;</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;};</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160; </div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;template&lt;typename Derived, typename XprKind = typename traits&lt;Derived&gt;::XprKind, <span class="keyword">typename</span> StorageKind = <span class="keyword">typename</span> traits&lt;Derived&gt;::StorageKind&gt;</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;<span class="keyword">struct </span>generic_xpr_base;</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160; </div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived, <span class="keyword">typename</span> XprKind&gt;</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;<span class="keyword">struct </span>generic_xpr_base&lt;Derived, XprKind, Dense&gt;</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;{</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> dense_xpr_base&lt;Derived,XprKind&gt;::type type;</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;};</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160; </div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> XprType, <span class="keyword">typename</span> CastType&gt; <span class="keyword">struct </span>cast_return_type</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;{</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> XprType::Scalar CurrentScalarType;</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="keyword">typedef</span> remove_all_t&lt;CastType&gt; CastType_;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CastType_::Scalar NewScalarType;</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;is_same&lt;CurrentScalarType,NewScalarType&gt;::value,</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;                              <span class="keyword">const</span> XprType&amp;,CastType&gt; type;</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;};</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160; </div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> B&gt; <span class="keyword">struct </span>promote_storage_type;</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160; </div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A&gt; <span class="keyword">struct </span>promote_storage_type&lt;A,A&gt;</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;{</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  <span class="keyword">typedef</span> A ret;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;};</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A&gt; <span class="keyword">struct </span>promote_storage_type&lt;A, const A&gt;</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;{</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;  <span class="keyword">typedef</span> A ret;</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;};</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A&gt; <span class="keyword">struct </span>promote_storage_type&lt;const A, A&gt;</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;{</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;  <span class="keyword">typedef</span> A ret;</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;};</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160; </div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> B, <span class="keyword">typename</span> Functor&gt; <span class="keyword">struct </span>cwise_promote_storage_type;</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160; </div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> Functor&gt;                   <span class="keyword">struct </span>cwise_promote_storage_type&lt;A,A,Functor&gt;                                      { <span class="keyword">typedef</span> A      ret; };</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Functor&gt;                               <span class="keyword">struct </span>cwise_promote_storage_type&lt;Dense,Dense,Functor&gt;                              { <span class="keyword">typedef</span> Dense  ret; };</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> Functor&gt;                   <span class="keyword">struct </span>cwise_promote_storage_type&lt;A,Dense,Functor&gt;                                  { <span class="keyword">typedef</span> Dense  ret; };</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> B, <span class="keyword">typename</span> Functor&gt;                   <span class="keyword">struct </span>cwise_promote_storage_type&lt;Dense,B,Functor&gt;                                  { <span class="keyword">typedef</span> Dense  ret; };</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Functor&gt;                               <span class="keyword">struct </span>cwise_promote_storage_type&lt;Sparse,Dense,Functor&gt;                             { <span class="keyword">typedef</span> Sparse ret; };</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Functor&gt;                               <span class="keyword">struct </span>cwise_promote_storage_type&lt;Dense,Sparse,Functor&gt;                             { <span class="keyword">typedef</span> Sparse ret; };</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160; </div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> LhsKind, <span class="keyword">typename</span> RhsKind, <span class="keywordtype">int</span> LhsOrder, <span class="keywordtype">int</span> RhsOrder&gt; <span class="keyword">struct </span>cwise_promote_storage_order {</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  <span class="keyword">enum</span> { value = LhsOrder };</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;};</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160; </div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> LhsKind, <span class="keywordtype">int</span> LhsOrder, <span class="keywordtype">int</span> RhsOrder&gt;   <span class="keyword">struct </span>cwise_promote_storage_order&lt;LhsKind,Sparse,LhsOrder,RhsOrder&gt;                { <span class="keyword">enum</span> { value = RhsOrder }; };</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> RhsKind, <span class="keywordtype">int</span> LhsOrder, <span class="keywordtype">int</span> RhsOrder&gt;   <span class="keyword">struct </span>cwise_promote_storage_order&lt;Sparse,RhsKind,LhsOrder,RhsOrder&gt;                { <span class="keyword">enum</span> { value = LhsOrder }; };</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> Order&gt;                                      <span class="keyword">struct </span>cwise_promote_storage_order&lt;Sparse,Sparse,Order,Order&gt;                       { <span class="keyword">enum</span> { value = Order }; };</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160; </div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160; </div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keyword">typename</span> B, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type;</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160; </div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;A,                  A,                  ProductTag&gt; { <span class="keyword">typedef</span> A     ret;};</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> ProductTag&gt;             <span class="keyword">struct </span>product_promote_storage_type&lt;Dense,              Dense,              ProductTag&gt; { <span class="keyword">typedef</span> Dense ret;};</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;A,                  Dense,              ProductTag&gt; { <span class="keyword">typedef</span> Dense ret; };</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> B, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;Dense,              B,                  ProductTag&gt; { <span class="keyword">typedef</span> Dense ret; };</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160; </div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;A,                  DiagonalShape,      ProductTag&gt; { <span class="keyword">typedef</span> A ret; };</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> B, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;DiagonalShape,      B,                  ProductTag&gt; { <span class="keyword">typedef</span> B ret; };</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> ProductTag&gt;             <span class="keyword">struct </span>product_promote_storage_type&lt;Dense,              DiagonalShape,      ProductTag&gt; { <span class="keyword">typedef</span> Dense ret; };</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> ProductTag&gt;             <span class="keyword">struct </span>product_promote_storage_type&lt;DiagonalShape,      Dense,              ProductTag&gt; { <span class="keyword">typedef</span> Dense ret; };</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160; </div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> A, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;A,                  PermutationStorage, ProductTag&gt; { <span class="keyword">typedef</span> A ret; };</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> B, <span class="keywordtype">int</span> ProductTag&gt; <span class="keyword">struct </span>product_promote_storage_type&lt;PermutationStorage, B,                  ProductTag&gt; { <span class="keyword">typedef</span> B ret; };</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> ProductTag&gt;             <span class="keyword">struct </span>product_promote_storage_type&lt;Dense,              PermutationStorage, ProductTag&gt; { <span class="keyword">typedef</span> Dense ret; };</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> ProductTag&gt;             <span class="keyword">struct </span>product_promote_storage_type&lt;PermutationStorage, Dense,              ProductTag&gt; { <span class="keyword">typedef</span> Dense ret; };</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160; </div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExpressionType, <span class="keyword">typename</span> Scalar = <span class="keyword">typename</span> ExpressionType::Scalar&gt;</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;<span class="keyword">struct </span>plain_row_type</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;{</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, 1, ExpressionType::ColsAtCompileTime,</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;                 int(ExpressionType::PlainObject::Options) | int(<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>), 1, ExpressionType::MaxColsAtCompileTime&gt; MatrixRowType;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;  <span class="keyword">typedef</span> Array&lt;Scalar, 1, ExpressionType::ColsAtCompileTime,</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;                 int(ExpressionType::PlainObject::Options) | int(<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>), 1, ExpressionType::MaxColsAtCompileTime&gt; ArrayRowType;</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160; </div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;    is_same&lt; typename traits&lt;ExpressionType&gt;::XprKind, MatrixXpr &gt;::value,</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;    MatrixRowType,</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;    ArrayRowType</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;  &gt; type;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;};</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160; </div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExpressionType, <span class="keyword">typename</span> Scalar = <span class="keyword">typename</span> ExpressionType::Scalar&gt;</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;<span class="keyword">struct </span>plain_col_type</div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;{</div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, ExpressionType::RowsAtCompileTime, 1,</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;                 ExpressionType::PlainObject::Options &amp; ~<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>, ExpressionType::MaxRowsAtCompileTime, 1&gt; MatrixColType;</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;  <span class="keyword">typedef</span> Array&lt;Scalar, ExpressionType::RowsAtCompileTime, 1,</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;                 ExpressionType::PlainObject::Options &amp; ~<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>, ExpressionType::MaxRowsAtCompileTime, 1&gt; ArrayColType;</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160; </div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;    is_same&lt; typename traits&lt;ExpressionType&gt;::XprKind, MatrixXpr &gt;::value,</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;    MatrixColType,</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;    ArrayColType</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  &gt; type;</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;};</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160; </div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExpressionType, <span class="keyword">typename</span> Scalar = <span class="keyword">typename</span> ExpressionType::Scalar&gt;</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;<span class="keyword">struct </span>plain_diag_type</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;{</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;  <span class="keyword">enum</span> { diag_size = internal::min_size_prefer_dynamic(ExpressionType::RowsAtCompileTime, ExpressionType::ColsAtCompileTime),</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;         max_diag_size = min_size_prefer_fixed(ExpressionType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;                                               ExpressionType::MaxColsAtCompileTime)</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;  };</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;Scalar, diag_size, 1, ExpressionType::PlainObject::Options &amp; ~RowMajor, max_diag_size, 1&gt; MatrixDiagType;</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  <span class="keyword">typedef</span> Array&lt;Scalar, diag_size, 1, ExpressionType::PlainObject::Options &amp; ~RowMajor, max_diag_size, 1&gt; ArrayDiagType;</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160; </div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  <span class="keyword">typedef</span> std::conditional_t&lt;</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;    is_same&lt; typename traits&lt;ExpressionType&gt;::XprKind, MatrixXpr &gt;::value,</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;    MatrixDiagType,</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;    ArrayDiagType</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;  &gt; type;</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;};</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160; </div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Expr,<span class="keyword">typename</span> Scalar = <span class="keyword">typename</span> Expr::Scalar&gt;</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;<span class="keyword">struct </span>plain_constant_type</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;{</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  <span class="keyword">enum</span> { Options = (traits&lt;Expr&gt;::Flags&amp;<a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>)?<a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a>:0 };</div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160; </div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1DenseBase.html#a277fac61f255b4438689daa78aa2028eadb37c78ebbf15aa20b65c3b70415a1ab">Array&lt;Scalar,  traits&lt;Expr&gt;::RowsAtCompileTime</a>,   traits&lt;Expr&gt;::ColsAtCompileTime,</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;                Options, traits&lt;Expr&gt;::MaxRowsAtCompileTime,traits&lt;Expr&gt;::MaxColsAtCompileTime&gt; array_type;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160; </div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1DenseBase.html#a277fac61f255b4438689daa78aa2028eadb37c78ebbf15aa20b65c3b70415a1ab">Matrix&lt;Scalar,  traits&lt;Expr&gt;::RowsAtCompileTime</a>,   traits&lt;Expr&gt;::ColsAtCompileTime,</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;                 Options, traits&lt;Expr&gt;::MaxRowsAtCompileTime,traits&lt;Expr&gt;::MaxColsAtCompileTime&gt; matrix_type;</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160; </div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;  <span class="keyword">typedef</span> CwiseNullaryOp&lt;scalar_constant_op&lt;Scalar&gt;, <span class="keyword">const</span> std::conditional_t&lt;is_same&lt; typename traits&lt;Expr&gt;::XprKind, MatrixXpr &gt;::value, matrix_type, array_type&gt; &gt; type;</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;};</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160; </div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ExpressionType&gt;</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;<span class="keyword">struct </span>is_lvalue</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;{</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;  <span class="keyword">enum</span> { value = (!bool(is_const&lt;ExpressionType&gt;::value)) &amp;&amp;</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;                 <span class="keywordtype">bool</span>(traits&lt;ExpressionType&gt;::Flags &amp; <a class="code" href="group__flags.html#gae2c323957f20dfdc6cb8f44428eaec1a">LvalueBit</a>) };</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;};</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160; </div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>is_diagonal</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;{ <span class="keyword">enum</span> { ret = <span class="keyword">false</span> }; };</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160; </div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>is_diagonal&lt;DiagonalBase&lt;T&gt; &gt;</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;{ <span class="keyword">enum</span> { ret = <span class="keyword">true</span> }; };</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160; </div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>is_diagonal&lt;DiagonalWrapper&lt;T&gt; &gt;</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;{ <span class="keyword">enum</span> { ret = <span class="keyword">true</span> }; };</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160; </div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keywordtype">int</span> S&gt; <span class="keyword">struct </span>is_diagonal&lt;DiagonalMatrix&lt;T,S&gt; &gt;</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;{ <span class="keyword">enum</span> { ret = <span class="keyword">true</span> }; };</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160; </div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160; </div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>is_identity</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;{ <span class="keyword">enum</span> { value = <span class="keyword">false</span> }; };</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160; </div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T&gt; <span class="keyword">struct </span>is_identity&lt;CwiseNullaryOp&lt;internal::scalar_identity_op&lt;typename T::Scalar&gt;, T&gt; &gt;</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;{ <span class="keyword">enum</span> { value = <span class="keyword">true</span> }; };</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160; </div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160; </div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> S1, <span class="keyword">typename</span> S2&gt; <span class="keyword">struct </span>glue_shapes;</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>glue_shapes&lt;DenseShape,TriangularShape&gt; { <span class="keyword">typedef</span> TriangularShape type;  };</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160; </div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T1, <span class="keyword">typename</span> T2&gt;</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;<span class="keyword">struct </span>possibly_same_dense {</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  <span class="keyword">enum</span> { value = has_direct_access&lt;T1&gt;::ret &amp;&amp; has_direct_access&lt;T2&gt;::ret &amp;&amp; is_same&lt;typename T1::Scalar,typename T2::Scalar&gt;::value };</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;};</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160; </div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T1, <span class="keyword">typename</span> T2&gt;</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;<span class="keywordtype">bool</span> is_same_dense(<span class="keyword">const</span> T1 &amp;mat1, <span class="keyword">const</span> T2 &amp;mat2, std::enable_if_t&lt;possibly_same_dense&lt;T1,T2&gt;::value&gt; * = 0)</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;{</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;  <span class="keywordflow">return</span> (mat1.data()==mat2.data()) &amp;&amp; (mat1.innerStride()==mat2.innerStride()) &amp;&amp; (mat1.outerStride()==mat2.outerStride());</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;}</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160; </div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T1, <span class="keyword">typename</span> T2&gt;</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;EIGEN_DEVICE_FUNC</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;<span class="keywordtype">bool</span> is_same_dense(<span class="keyword">const</span> T1 &amp;, <span class="keyword">const</span> T2 &amp;, std::enable_if_t&lt;!possibly_same_dense&lt;T1,T2&gt;::value&gt; * = 0)</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;{</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;}</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160; </div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;<span class="comment">// Internal helper defining the cost of a scalar division for the type T.</span></div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;<span class="comment">// The default heuristic can be specialized for each scalar type and architecture.</span></div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T,<span class="keywordtype">bool</span> Vectorized=false,<span class="keyword">typename</span> EnableIf = <span class="keywordtype">void</span>&gt;</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;<span class="keyword">struct </span>scalar_div_cost {</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;  <span class="keyword">enum</span> { value = 8*NumTraits&lt;T&gt;::MulCost };</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;};</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160; </div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T,<span class="keywordtype">bool</span> Vectorized&gt;</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;<span class="keyword">struct </span>scalar_div_cost&lt;std::complex&lt;T&gt;, Vectorized&gt; {</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;  <span class="keyword">enum</span> { value = 2*scalar_div_cost&lt;T&gt;::value</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;               + 6*NumTraits&lt;T&gt;::MulCost</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;               + 3*NumTraits&lt;T&gt;::AddCost</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;  };</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;};</div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160; </div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160; </div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Vectorized&gt;</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;<span class="keyword">struct </span>scalar_div_cost&lt;signed long,Vectorized, std::conditional_t&lt;sizeof(long)==8,void,false_type&gt;&gt; { <span class="keyword">enum</span> { value = 24 }; };</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Vectorized&gt;</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;<span class="keyword">struct </span>scalar_div_cost&lt;unsigned long,Vectorized, std::conditional_t&lt;sizeof(long)==8,void,false_type&gt;&gt; { <span class="keyword">enum</span> { value = 21 }; };</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160; </div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160; </div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;<span class="preprocessor">#ifdef EIGEN_DEBUG_ASSIGN</span></div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;std::string demangle_traversal(<span class="keywordtype">int</span> t)</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;{</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;  <span class="keywordflow">if</span>(t==DefaultTraversal) <span class="keywordflow">return</span> <span class="stringliteral">&quot;DefaultTraversal&quot;</span>;</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;  <span class="keywordflow">if</span>(t==LinearTraversal) <span class="keywordflow">return</span> <span class="stringliteral">&quot;LinearTraversal&quot;</span>;</div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="keywordflow">if</span>(t==InnerVectorizedTraversal) <span class="keywordflow">return</span> <span class="stringliteral">&quot;InnerVectorizedTraversal&quot;</span>;</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;  <span class="keywordflow">if</span>(t==LinearVectorizedTraversal) <span class="keywordflow">return</span> <span class="stringliteral">&quot;LinearVectorizedTraversal&quot;</span>;</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;  <span class="keywordflow">if</span>(t==SliceVectorizedTraversal) <span class="keywordflow">return</span> <span class="stringliteral">&quot;SliceVectorizedTraversal&quot;</span>;</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;  <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;}</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;std::string demangle_unrolling(<span class="keywordtype">int</span> t)</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;{</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;  <span class="keywordflow">if</span>(t==NoUnrolling) <span class="keywordflow">return</span> <span class="stringliteral">&quot;NoUnrolling&quot;</span>;</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;  <span class="keywordflow">if</span>(t==InnerUnrolling) <span class="keywordflow">return</span> <span class="stringliteral">&quot;InnerUnrolling&quot;</span>;</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;  <span class="keywordflow">if</span>(t==CompleteUnrolling) <span class="keywordflow">return</span> <span class="stringliteral">&quot;CompleteUnrolling&quot;</span>;</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;  <span class="keywordflow">return</span> <span class="stringliteral">&quot;?&quot;</span>;</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;}</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;std::string demangle_flags(<span class="keywordtype">int</span> f)</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;{</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;  std::string res;</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;  <span class="keywordflow">if</span>(f&amp;<a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a>)                 res += <span class="stringliteral">&quot; | RowMajor&quot;</span>;</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;  <span class="keywordflow">if</span>(f&amp;<a class="code" href="group__flags.html#ga1a306a438e1ab074e8be59512e887b9f">PacketAccessBit</a>)             res += <span class="stringliteral">&quot; | Packet&quot;</span>;</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;  <span class="keywordflow">if</span>(f&amp;<a class="code" href="group__flags.html#ga4b983a15d57cd55806df618ac544d09e">LinearAccessBit</a>)             res += <span class="stringliteral">&quot; | Linear&quot;</span>;</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160;  <span class="keywordflow">if</span>(f&amp;<a class="code" href="group__flags.html#gae2c323957f20dfdc6cb8f44428eaec1a">LvalueBit</a>)                   res += <span class="stringliteral">&quot; | Lvalue&quot;</span>;</div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;  <span class="keywordflow">if</span>(f&amp;<a class="code" href="group__flags.html#gabf1e9d0516a933445a4c307ad8f14915">DirectAccessBit</a>)             res += <span class="stringliteral">&quot; | Direct&quot;</span>;</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;  <span class="keywordflow">if</span>(f&amp;NestByRefBit)                res += <span class="stringliteral">&quot; | NestByRef&quot;</span>;</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;  <span class="keywordflow">if</span>(f&amp;<a class="code" href="group__flags.html#ga3c186ad80ddcf5e2ed3d7ee31cca1860">NoPreferredStorageOrderBit</a>)  res += <span class="stringliteral">&quot; | NoPreferredStorageOrderBit&quot;</span>;</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160; </div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;}</div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160; </div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160; </div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160; </div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> ScalarA, <span class="keyword">typename</span> ScalarB, <span class="keyword">typename</span> BinaryOp=<span class="keywordtype">int</span>ernal::scalar_product_op&lt;ScalarA,ScalarB&gt; &gt;</div>
<div class="line"><a name="l00769"></a><span class="lineno"><a class="line" href="structEigen_1_1ScalarBinaryOpTraits.html">  769</a></span>&#160;<span class="keyword">struct </span><a class="code" href="structEigen_1_1ScalarBinaryOpTraits.html">ScalarBinaryOpTraits</a></div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;#ifndef EIGEN_PARSED_BY_DOXYGEN</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;  <span class="comment">// for backward compatibility, use the hints given by the (deprecated) internal::scalar_product_traits class.</span></div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160;  : internal::scalar_product_traits&lt;ScalarA,ScalarB&gt;</div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;{};</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160; </div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> BinaryOp&gt;</div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;<span class="keyword">struct </span><a class="code" href="structEigen_1_1ScalarBinaryOpTraits.html">ScalarBinaryOpTraits</a>&lt;T,T,BinaryOp&gt;</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160;{</div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;  <span class="keyword">typedef</span> T ReturnType;</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160;};</div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160; </div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> BinaryOp&gt;</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;T, typename NumTraits&lt;std::enable_if_t&lt;NumTraits&lt;T&gt;::IsComplex,T&gt;&gt;::Real, BinaryOp&gt;</div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;{</div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;  <span class="keyword">typedef</span> T ReturnType;</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160;};</div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> BinaryOp&gt;</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;typename NumTraits&lt;std::enable_if_t&lt;NumTraits&lt;T&gt;::IsComplex,T&gt;&gt;::Real, T, BinaryOp&gt;</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160;{</div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;  <span class="keyword">typedef</span> T ReturnType;</div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;};</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160; </div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;<span class="comment">// For Matrix * Permutation</span></div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> BinaryOp&gt;</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;T,void,BinaryOp&gt;</div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;{</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160;  <span class="keyword">typedef</span> T ReturnType;</div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;};</div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160; </div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;<span class="comment">// For Permutation * Matrix</span></div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> T, <span class="keyword">typename</span> BinaryOp&gt;</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;void,T,BinaryOp&gt;</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;{</div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;  <span class="keyword">typedef</span> T ReturnType;</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;};</div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160; </div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;<span class="comment">// for Permutation*Permutation</span></div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> BinaryOp&gt;</div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;<span class="keyword">struct </span>ScalarBinaryOpTraits&lt;void,void,BinaryOp&gt;</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;{</div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;  <span class="keyword">typedef</span> <span class="keywordtype">void</span> ReturnType;</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160;};</div>
<div class="line"><a name="l00813"></a><span class="lineno">  813</span>&#160; </div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;<span class="comment">// We require Lhs and Rhs to have &quot;compatible&quot; scalar types.</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;<span class="comment">// It is tempting to always allow mixing different types but remember that this is often impossible in the vectorized paths.</span></div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;<span class="comment">// So allowing mixing different types gives very unexpected errors when enabling vectorization, when the user tries to</span></div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;<span class="comment">// add together a float matrix and a double matrix.</span></div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;<span class="preprocessor">#define EIGEN_CHECK_BINARY_COMPATIBILIY(BINOP,LHS,RHS) \</span></div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;<span class="preprocessor">  EIGEN_STATIC_ASSERT((Eigen::internal::has_ReturnType&lt;ScalarBinaryOpTraits&lt;LHS, RHS,BINOP&gt; &gt;::value), \</span></div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;<span class="preprocessor">    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)</span></div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160; </div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160; </div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_XPRHELPER_H</span></div>
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<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">Eigen::ColMajor</a></div><div class="ttdeci">@ ColMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:321</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">Eigen::RowMajor</a></div><div class="ttdeci">@ RowMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:323</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea">Eigen::AutoAlign</a></div><div class="ttdeci">@ AutoAlign</div><div class="ttdef"><b>Definition:</b> Constants.h:325</div></div>
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<div class="ttc" id="agroup__flags_html_ga4b983a15d57cd55806df618ac544d09e"><div class="ttname"><a href="group__flags.html#ga4b983a15d57cd55806df618ac544d09e">Eigen::LinearAccessBit</a></div><div class="ttdeci">const unsigned int LinearAccessBit</div><div class="ttdef"><b>Definition:</b> Constants.h:132</div></div>
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<div class="ttc" id="agroup__flags_html_gae2c323957f20dfdc6cb8f44428eaec1a"><div class="ttname"><a href="group__flags.html#gae2c323957f20dfdc6cb8f44428eaec1a">Eigen::LvalueBit</a></div><div class="ttdeci">const unsigned int LvalueBit</div><div class="ttdef"><b>Definition:</b> Constants.h:146</div></div>
<div class="ttc" id="agroup__flags_html_gae4f56c2a60bbe4bd2e44c5b19cbe8762"><div class="ttname"><a href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">Eigen::RowMajorBit</a></div><div class="ttdeci">const unsigned int RowMajorBit</div><div class="ttdef"><b>Definition:</b> Constants.h:68</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
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<div class="ttc" id="astructEigen_1_1ScalarBinaryOpTraits_html"><div class="ttname"><a href="structEigen_1_1ScalarBinaryOpTraits.html">Eigen::ScalarBinaryOpTraits</a></div><div class="ttdoc">Determines whether the given binary operation of two numeric types is allowed and what the scalar ret...</div><div class="ttdef"><b>Definition:</b> XprHelper.h:774</div></div>
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